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» On the Number of Halving Planes
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JAL
2006
100views more  JAL 2006»
13 years 9 months ago
Distance and routing labeling schemes for non-positively curved plane graphs
Distance labeling schemes are schemes that label the vertices of a graph with short labels in such a way that the distance between any two vertices u and v can be determined effic...
Victor Chepoi, Feodor F. Dragan, Yann Vaxès
GD
2006
Springer
14 years 1 months ago
Planar Decompositions and the Crossing Number of Graphs with an Excluded Minor
Tree decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. Planar decompositions generalise tree decompositions by allowing an arbitrar...
David R. Wood, Jan Arne Telle
WG
2010
Springer
13 years 8 months ago
Graphs with Large Obstacle Numbers
Motivated by questions in computer vision and sensor networks, Alpert et al. [3] introduced the following definitions. Given a graph G, an obstacle representation of G is a set of...
Padmini Mukkamala, János Pach, Deniz Sari&o...
JCT
2007
97views more  JCT 2007»
13 years 9 months ago
What power of two divides a weighted Catalan number?
Given a sequence of integers b = (b0,b1,b2,...) one gives a Dyck path P of length 2n the weight wt(P) = bh1 bh2 ···bhn , where hi is the height of the ith ascent of P. The corr...
Alexander Postnikov, Bruce E. Sagan
JGT
2010
113views more  JGT 2010»
13 years 8 months ago
Crossing numbers of imbalanced graphs
The crossing number, cr(G), of a graph G is the least number of crossing points in any drawing of G in the plane. According to the Crossing Lemma of Ajtai, Chv´atal, Newborn, Sze...
János Pach, József Solymosi, G&aacut...